Automatically Differentiable Random Coefficient Logistic Demand Estimation
This work addresses demand estimation in economics by improving computational efficiency and accuracy, though it is incremental as it builds on existing BLP models and estimation techniques.
The paper tackles the estimation of random coefficient logistic demand models by reformulating them as automatically differentiable moment functions, enabling gradient-based estimation with the Continuously Updating Estimator (CUE). Results show that CUE with LTE and frequentist optimization has lower bias but higher MAE than traditional 2S-GMM, and a hybrid approach using credible intervals and analytical standard errors achieves empirical coverage closest to nominal levels.
We show how the random coefficient logistic demand (BLP) model can be phrased as an automatically differentiable moment function, including the incorporation of numerical safeguards proposed in the literature. This allows gradient-based frequentist and quasi-Bayesian estimation using the Continuously Updating Estimator (CUE). Drawing from the machine learning literature, we outline hitherto under-utilized best practices in both frequentist and Bayesian estimation techniques. Our Monte Carlo experiments compare the performance of CUE, 2S-GMM, and LTE estimation. Preliminary findings indicate that the CUE estimated using LTE and frequentist optimization has a lower bias but higher MAE compared to the traditional 2-Stage GMM (2S-GMM) approach. We also find that using credible intervals from MCMC sampling for the non-linear parameters together with frequentist analytical standard errors for the concentrated out linear parameters provides empirical coverage closest to the nominal level. The accompanying admest Python package provides a platform for replication and extensibility.